2011/04/27 by V. F. Pisarenko, D. Sornette · 2 citations
Physics and Astronomy · #physics.data-an #nlin.AO
paper · pdf · doi:10.1140/epjst/e2012-01564-8
published as Eur. Phys. J. Special Topics 205, 95-115 (2012) · 30 pages, 21 figures, 3 tables
arxiv created 2011/04/27 · arxiv updated 2015/05/28
We ask the question whether it is possible to diagnose the existence of "Dragon-Kings" (DK), namely anomalous observations compared to a power law background distribution of event sizes. We present two new statistical tests, the U-test and the DK-test, aimed at identifying the existence of even a single anomalous event in the tail of the distribution of just a few tens of observations. The DK-test in particular is derived such that the p-value of its statistic is independent of the exponent characterizing the null hypothesis. We demonstrate how to apply these two tests on the distributions of cities and of agglomerations in a number of countries. We find the following evidence for Dragon-Kings: London in the distribution of city sizes of Great Britain; Moscow and St-Petersburg in the distribution of city sizes in the Russian Federation; and Paris in the distribution of agglomeration sizes in France. True negatives are also reported, for instance the absence of Dragon-Kings in the distribution of cities in Germany.